So I'm confused; What exactly did Zukos' mom do to get banished?

well, since 你 say 你 watched the episode many, many times 你 should know what i'm talking about.

Ozai didn't like that fact that his older brother, Iroh, was going to become firelord. Since Iroh 迷失 his only son, Luten, to Ozai, he became weak. He had a meeting with his father, Firelord Azulan, telling him that Iroh's only son had died and that his blood line had ended, but his was still well and alive.
Angered 由 what Ozai had 说 he told him that Iroh had 迷失 his only son, his first born and that Ozai should experience the same thing, he would have to Kill Zuko. Ursula, zuko's mom, had found out about the conversation and basically confronted Ozai. So she made a deal with him, Ursula would kill the firelord so that Ozai would spare Zuko. So she did what she had to do to protect Zuko, and for that she was banished.

yeah i know i'm not very easy to understand but yeah anyways hopped i helped?! i know really long too, sorry!

The specific details of the plan are not spelled out, but it resulted in the death of Azulon and Ozai's ascension to the 火, 消防 Nation 王座, 宝座 in Iroh's place. She was then banished from the 火, 消防 Nation for doing "vicious, treasonous things" (with the implication that she either assassinated Azulon herself, 或者 else caused it to be done)...................Hope it 答案 your 问题

yes.i feeling too.

she took zuko's place,Zuko was suppose to be killed 由 his father Ozai,as a punnishment from 火, 消防 lord azulon ,Ozai suggested that he should be 下一个 in line 2 be 火, 消防 lord since Iroh did not seem 2 be capeble due to his son's death.Azulon thought that this was unthoughtful of him, so he orderd ozai to kill his son,zuko's mom heard about this & decided to take his place. she was never killed of corse,ozai mentions this in the last episode book 3,when zuko visits ozai in prison.

because ursa proposed of a plan that would make ozai the firelord and zuko alive so the plan was to kill azulon and ozai to regain power but after the death of azulon ursa was banished from the palace because she was the only one who knew about it